try setting your TCP/IP properties DNS entries to like OPENDNS [https://store.opendns.com/setup/] and see if that fixes it or not, if not change it back to get automatically from ISP. That would be one of the things that would differ from a gaming server, the gaming server will connect by DIRECT IP, the web uses DNS to look up IP's from things like www.google.com before connection and a bad DNS can take forever.
The other case where I see this is double NAT [which I believe if related to double NAT with double DNS, but not certain], but you'd have to be chaining routers to cause this.